Problem: Solve for $n$, $ \dfrac{3n}{9n - 6} = \dfrac{7}{9n - 6} - \dfrac{1}{3n - 2} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $9n - 6$ $9n - 6$ and $3n - 2$ The common denominator is $9n - 6$ The denominator of the first term is already $9n - 6$ , so we don't need to change it. The denominator of the second term is already $9n - 6$ , so we don't need to change it. To get $9n - 6$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{1}{3n - 2} \times \dfrac{3}{3} = -\dfrac{3}{9n - 6} $ This give us: $ \dfrac{3n}{9n - 6} = \dfrac{7}{9n - 6} - \dfrac{3}{9n - 6} $ If we multiply both sides of the equation by $9n - 6$ , we get: $ 3n = 7 - 3$ $ 3n = 4$ $ 3n = 4 $ $ n = \dfrac{4}{3}$